December 20, 2007, Sergey Bastrukov

Elastic Vibrations of Atomic Nuclei and Neutron Stars

Brief review of elastodynamical approach to the continuum mechanics of nuclear matter

Atomic nuclei (heavier than Fe-56) and neutron stars are products of Atomic nuclei (heavier than Fe-56) and neutron stars are products of supernova explosion. The identical density and similar nucleonic supernova explosion. The identical density and similar nucleonic composition suggest that they can be regarded as small and big composition suggest that they can be regarded as small and big samples of one and the same in material properties nucleon samples of one and the same in material properties nucleon condensed matter.condensed matter.

Z=114-118Dubna

Z=114-118Dubna

Z=110-112Darmstadt

The current investigations on nuclear physics and pulsar astrophysics suggest that the Fermi-degenerate nucleon condensed matter constituting interior of atomic nuclei and the main body of neutron stars possesses properties of solid-mechanical shear elasticity and shear viscosity.

In nuclear physics, the Solid Globe Model has been invoked to explain electric and magnetic giant-resonant excitations in terms of spheroidal and torsional shear vibrations of viscoelastic solid sphere.

In pulsar astrophysics, the Solid Star Model is currently utilized to explain the detected millisecond quasi-periodic oscillations in electromagnetic spectra of pulsars and magnetars in terms of torsional elastic vibrations.

Continuous Nuclear Matter as Viscoelastic Fermi-solid

The empirically established general trends in data on energy centroid of giant resonances throughout periodic table are properly described in terms of shear vibrations of an elastic sphere This implies that Fermi-degenerate nucleon material can be specified as elastic Fermi-solid.

Electric giant resonances can be interpreted as spheroidal shear vibrations of femtoparticle of an elastic Fermi-continuum

Abstract  The nuclear fluid-dynamical Hamiltonian which takes the distortion of the local Fermi surface into account predicts the Twist mode (T=0, J=2–) at a finite frequency (about 7.5 MeV for208Pb).The application of our non-Newtonian nuclear fluid dynamics to the Twist was initiated by M.Danos, who kindly informed one of the authors (G.H.) about early attempts of J.H.D.Jensen to obtain a nuclear twisting mode within Newtonian hydrodynamics.

The nuclear “Twist”

Magnetic quadrupole resonance can be thought of as an eigenmodeof torsional quadrupole oscillations driven by restoring force of elastic stresses

Magnetic giant resonances as eigenmodes of torsional elastic vibrations

Viscosity of nuclear matter

The widths of resonances carry information aboutviscosity of nuclear matter

Nuclear Solid Globe Model Nuclear Solid Globe Model

Ring-like distribution of sites about of which the nucleons undergozero-point oscillations and exchangeplaces. The nucleons are not localizedbut are in the state of incessant quantum-wave motions which is described as ordered Fermi-motion of independent nucleon-like quasi-particle in the nuclear mean field.

Nuclear Solid Globe Nuclear Solid Globe ModelModel

From standpoint of the solid globe model the fast nuclear response by From standpoint of the solid globe model the fast nuclear response by giant electric resonances is associated with irrotational shear giant electric resonances is associated with irrotational shear deformational oscillations of orbits preserving their closed shape and deformational oscillations of orbits preserving their closed shape and by giant magnetic resonances differentially – rotational oscillations of by giant magnetic resonances differentially – rotational oscillations of orbits with respect each other. In the process of these oscillations the orbits with respect each other. In the process of these oscillations the energy order of single-particle states in the potential of nuclear mean energy order of single-particle states in the potential of nuclear mean field of shell model is unchanged.field of shell model is unchanged.

Fundamental modes of quasi-static nodeless

elastic shear vibrations of solid sphere

Experimental manifestation of solid-mechanical viscoelasticity of nuclear matter in the electromagnetic response of atomic nuclei

by giant resonances

Dipole Spheroidal and Dipole Torsional modes emerge when perturbation sets in oscillations peripheral layer whereas internal undisturbed region remains immobilized. This case can be treated as elastic oscillations of peripheral layer against static core

Starquake

X-ray flare ~ 100-300 sec

Quasi-periodic oscillations of x-ray lumioisity

Dipole spheroidal and torsional oscillations of the crust against coreare Goldstone modes vanishing when the all volume of the star sets in vibrations. The case when h=1.

QPOs of lowest frequency are due to dipole spheroidal and torsional elastic shear vibrations of the crust against core